Erlinda Kartika Putri, Santi Irawati, Hidetoshi Marubayashi
A ring R is called strongly r-clean ring if every element x ∈ R can be written as x = r + e with re = er, for some regular element r and idempotent element e in R. This article aims to show all strongly r-clean elements in the certain ring of matrices T3(p2)={[a11¯0¯0¯0¯a22¯0¯a31¯0¯a33¯]aij¯∈p2;i,j=1,2,3} for any prime p. The research method is determining all idempotent elements and regular elements in T3(p2), (ii) constructing all the strongly r-clean elements. The result showed it can be constructed four general forms of idempotent elements and eight general forms of regular elements in T3(p2). Based on the existence of idempotent and regular elements, it can be constructed twenty general forms of strongly r-clean elements in T3(p2) for any prime p. © 2024 Author(s).
Mathematics Department, Universitas Negeri Malang, Malang, Indonesia; Department of Mathematics, Naruto University of Education, Naruto, Japan
